The biggest difference between green fluorescent protein and its red analog, DsRed, is that the chromophore of DsRed has an extra double bond (drawn in yellow) which extends the chromophores conjugation and causes the red-shift.

Reference:
RE Campbell, O Tour, AE Palmer, PA Steinbach, GS Baird, DA Zacharias, RY Tsien: A monomeric red fluorescent protein. Proceedings of the National Academy of Sciences of the United States of America 99 (2002) 7877-82.